Assessing the accuracy of TDR-based water leak detection system

Results in Physics 8 (2018) 939–948

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Assessing the accuracy of TDR-based water leak detection system S.M. Fatemi Aghda a, K. Ganjalipour a,⇑, K. Nabiollahi b a b

Department of Applied Geology, Faculty of Geological Science, Kharazmi University, Tehran, Iran Department of Soil Science and Engineering, University of Kurdistan, Iran

a r t i c l e

i n f o

Article history: Received 20 September 2017 Received in revised form 11 January 2018 Accepted 11 January 2018

Keywords: Multiple leakage points TDR Reference points

a b s t r a c t The use of TDR system to detect leakage locations in underground pipes has been developed in recent years. In this system, a bi-wire is installed in parallel with the underground pipes and is considered as a TDR sensor. This approach greatly covers the limitations arisen with using the traditional method of acoustic leak positioning. TDR based leak detection method is relatively accurate when the TDR sensor is in contact with water in just one point. Researchers have been working to improve the accuracy of this method in recent years. In this study, the ability of TDR method was evaluated in terms of the appearance of multi leakage points simultaneously. For this purpose, several laboratory tests were conducted. In these tests in order to simulate leakage points, the TDR sensor was put in contact with water at some points, then the number and the dimension of the simulated leakage points were gradually increased. The results showed that with the increase in the number and dimension of the leakage points, the error rate of the TDR-based water leak detection system increases. The authors tried, according to the results obtained from the laboratory tests, to develop a method to improve the accuracy of the TDR-based leak detection systems. To do that, they defined a few reference points on the TDR sensor. These points were created via increasing the distance between two conductors of TDR sensor and were easily identifiable in the TDR waveform. The tests were repeated again using the TDR sensor having reference points. In order to calculate the exact distance of the leakage point, the authors developed an equation in accordance to the reference points. A comparison between the results obtained from both tests (with and without reference points) showed that using the method and equation developed by the authors can significantly improve the accuracy of positioning the leakage points. Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction Daily losing of water in many cities consists of between 40 to 50% of consumption water which leads to environmental, economic, health, and safety costs [1–3]. Poor quality of materials used in manufacturing of pipes, planning errors, inadequate maintenance, applying the network in a high-pressure condition, and accidental damage are some of those causes for damages in water supply network [4]. In the United States 20 percent of water supply are being lost through leakage in pipeline [5]. The defect points of pipeline should be identified by suitable inspection tools. [6]. There are several economic techniques to detect leak points. Bose & Olson [7] and Turner [8] classified leakage detection methods in water pipes into three groups that include biological methods, hardware-based methods, and software-based methods [7–9]. ⇑ Corresponding author at: Department of Applied Geology, Faculty of Geological Science, Kharazmi University, Tehran 15815-3587, Iran. E-mail address: [email protected] (K. Ganjalipour).

In such a context, the possibility of carrying out frequent and efficient leak-localization campaigns is crucial for an effective water resource management. Traditional leak localization systems which are mostly based on acoustic methods, are time-consuming and their performance in positioning the leaks is affected by several factors including size, type, and depth of the pipe; soil type and water table level; leak type and size; system pressure; interfering noise; and sensitivity and frequency range of the equipment. Most professional users consider acoustic methods to be effective for finding leaks in metal pipes but problematic when used for plastic pipes. As a result, with traditional leak detection system, the choice of a particular technique depends on the specific conditions at hand [10]. To overcome these limitations, new technologies have been evaluated in order to achieve new methods. One of the technique attracted the researchers in recent years is Time Domain Reflectometry (TDR). This system is based on the electromagnetic measuring technique that is far from having the limitations of the traditional method of acoustic leak detection. The system requires

https://doi.org/10.1016/j.rinp.2018.01.027 2211-3797/Ó 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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a bi-wire cable attached to the pipes when installing them. In fact, in this system, the bi-wires is used as a sensing element connected to a measuring instrument to check whether there is a leak along the pipeline when necessary (Fig. 1). Since the TDR method is a new detection method of leakage points in pipes, it is necessary to evaluate its accuracy under different conditions and, if necessary, to improve its accuracy through innovative solutions. Although this technique is cheaper compared to other methods for the continuous monitoring of pipelines; however, it may impose additional cost to the user and could result the project become not cost-effective because of the lack of sufficient accuracy in detecting the location of the leakage. In studies carried out in the past, the accuracy of TDR method has been well evaluated in terms of the existence of just one leakage point, but so far, the effect of the number of leakage points on the accuracy of this method has not been seriously considered. The speed of electromagnetic wave is reduced when the TDR sensor get in the contact with the water. So it is natural that increasing number of leakage points tend to the accuracy of the system drop even more. In the event of multiple leaks, TDR system detects the nearest leak point to the TDR unit (first leak point) precisely, but for other leak points, it is not accurate due to the effect of leakage water on the pulse propagation speed. Therefore, the more the number of contact points of TDR cable with water, the less the accuracy of TDR system. In this study, first the authors evaluated the effect of multiple leaks and leakage expansion on the accuracy of the TDR-base leak localization system. Then, they developed a technique and an equation to detect and locate multiple leaks accurately. In the following, a summary of the theoretical foundations of the TDR method, the procedure of laboratory tests and their related results are presented. The theory of method TDR method is based on transmitting an electromagnetic pulse and measuring the delay time for reflecting back a part of the signal to the source point [11–13]. This pulse is a step signal of voltage with a very fast rise time that will be transmitted over the sensor and penetrates the test environment. The reflected signal has very useful information about the dielectric properties of materials surrounding the sensor. Therefore, the material qualita-

tive and quantitative properties can be detected with adequate data processing [14]. Kane & Beck [15]; Mikkelsen [16]; O, Connor & Dowding [17] used time domain reflectometry for monitoring slope movements and water level measurement [15–17]. TDR method has been used for many different applications, such as evaluation of dielectric and spectroscopic properties of materials [18–21]; qualitative and quantitative control of liquids [22,23,25]; examinations of vegetable oils [24–26]; cable fault detection [27,28]; and measurement of soil moisture [17,29,30]. In TDR measurements, the ratio between the amplitude of the signal that is reflected by the system under test (VR) and the amplitude of the generated signal (VI) will be displayed as reflection coefficient (q) [31].

q¼

Soil

Leakage position Pipe

ð2Þ

2L=T C

ð3Þ

2 1 v op

ð4Þ

v op ¼ e¼




where L indicates cable length (the use of 2L length is due to the pulse sweep over the sensor); T is the time required for the pulse to travel from the beginning of the cable to the end; C is the light speed in vacuum; and e is the dielectric constant of materials surrounding the bi-wire. One of the most important parameters of the cable is the characteristic impedance (Z0) and the reflection of electromagnetic pulses occurs due to the lack of impedance matching. The quantity of reflection coefficient can also be expressed in term of electrical impedance (Eq. (5)).

Z l ðdÞ  Z 0 Z l ðdÞ þ Z 0

276 2s Z 0 ¼ pffiffiffi log D k Reflection coefficient

Bi-wire

Schematic wave form

2L T

V cable ¼

ð5Þ

where Z0 is the characteristic impedance of the transmission line; and Zl is the load impedance at distance d and it depends on the effective dielectric permittivity of the transmission line at the considered section. For a bi-wire transmission line, the characteristic impedance is a function of the geometry, the size, the distance between two conductors and the dielectric constant of the insulation separating them from each other (Eq. (6)).

Ground surface

Lead cable

ð1Þ

TDR graphs are usually displayed as a plot of reflection coefficient against time. The most important benefit of TDR is that the reflection position and its causes are detected using transmission duration and reflection properties respectively. Dielectric constant of materials surrounding the bi-wire is a function of the electromagnetic wave transmission speed. This speed is usually expressed as a percentage of light speed in vacuum that is called VOP and is usually one of the cable specifications [20].

q¼ TDR Unit

VR VI

Distance Fig. 1. Schematization of the typical layout of an underground pipe equipped with the distributed bi-wire. The figure below shows a schematization of a typical reflectogram in presence of a leak [32].

ð6Þ

where k is the dielectric constant of insulation; s is the distance between two conductors; and D is the diameter of the conductor. So the reflection of electromagnetic pulse occurs in the position of dielectric change or geometry deformation. The location of these changes measured using the above mentioned equations. The TDR-based leak detection system exploits the physical principles of TDR-based investigation of materials. This leak detection technique is based on sensing the change of dielectric characteris-

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tics that occurs in the soil when water escapes from the pipe. The presence of water (whose relative (dielectric) permittivity is approximately equal to 80) provokes a local detectable change of the dielectric characteristics of the soil (whose relative permittivity- in dry conditions-does not usually exceed 2–3) [32]. In the use of TDR method as a leakage detector, a bi-wire cable is used as a TDR sensor installed along with the pipes while the materials surrounding the sensor play the role of the wave propagation environment. Leakage water changes the electrical characteristic of transmission line that can be identified well by means of TDR. The installation and application of the TDR has been shown in Fig. 1 schematically. In 2012 and 2013, Cataldo et al. conducted a series of experiments to validate the ability of TDR method in pinpointing water leak locations. The reported results from their experiments showed that TDR identify leak locations in underground pipes successfully. Also in 2014, they compared the ability of TDR, GPR, and electrical resistance tomography to detect leak locations in buried pipes. Again, they conducted some experiments in 2016 to detect the precise locations of leakage using TDR method. They installed a TDR sensor inside a water absorbent sponge and the experiment results showed that this method enhances the accuracy of leak localization. [32–34]. Description of the experimental equipment and discussion of the raw measurement results Description of the apparatus Research equipment consists of a TDR measuring device manufactured by Soil Moisture Company model 6050  1 and a bi-wire telecommunication cable used as TDR sensor. This apparatus generates a step pulse with an amplitude of 1.5 V and a rise time of 120 picoseconds. The output of the device is in the form of a BNC ports and its output impedance is 50 O. The BNC is a quick

connect/disconnect radio frequency connector. In this study, a bi-wire was used as TDR sensor. In a simple test, an electromagnetic pulse was transmitted into 13.7 m of bi-wire, and the VOP index was determined as 68.28%. In other words, the electromagnetic wave moved in the bi-wire used in this study as fast as 20.5 cm per nanoseconds (Fig. 2). Description of the laboratory measurement system and discussion on raw data As mentioned before, the dielectric constant of materials surrounding the TDR sensor is a function of the transmission speed of the electromagnetic wave in the bi-wire. Thus, the dielectric change of this materials influence the transmission speed of the electromagnetic wave in the bi-wire. With regards to that, the dielectric of water is high and there is a lot of difference between dielectric of water and other materials, the presence of water at any point along the transmission line has a great influence on the speed of the electromagnetic wave (reduces electromagnetic wave velocity). Therefore, the authors conducted two experiments (case 1 and 2) to test the effect of the multiple leaks and magnitude of contact zones of bi-wire with water on accuracy of TDRbased leak localization system. In order to simulate different leak conditions, the bi-wire cable was crossed through small water tanks and to simulate the leak points, these tanks were filled with water in such a way that the water surrounded the bi-wire completely (Fig. 3a). In the first experiment (case 1), TDR measurements were performed in four different conditions: (i) no point of bi-wire is in contact with the water (dry test); (ii) one point of bi-wire is in contact with water (point 1); (iii) two points of bi-wire are in contact with water (point 1, point 2),

End of the sensor

Beginning of the sensor

vop of the biwire T0 ( ns)

T1 (ns)

DT=T1-T0

L( cable lenght ) m

VCABLE m/ns

VOP %

3.200

70.080

66.880

13.700

0.205

68.28%

Fig. 2. The properties of the bi-wire used in this study (the time data in this study is required time for the pulse to travel in one direction from the start of the sensor to the end of the sensor (t/2)).

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Fig. 3. (a) Schematic diagram of the first experiment steps (case 1), (b) TDR reflectograms for: 1. No point of the cable is in contact with water, 2. One point of the cable is in contact with the water, 3. Two points of the cable are in contact with the water, and 4. Three points of the cable are in contact with water.

(iv) three points of bi-wire are in contact with water (point 1, point 2, and point 3), In this test, contact of the bi-wire with water at the point 1 was selected as the target point; therefore, the purpose of this test is assessing the effect of the number of the leakage points on the positioning accuracy of the target point, namely the point 1. First step condition, no leakage (no point of bi-wire is in contact with the water): At this step, all the water tanks were empty. In other words, no point of the bi-wire was in contact with the water. In this conditions, there is no minimum point in the waveform of the bi-wire. The waveform of the bi-wire cable at this condition can be considered as the base readings to compare with the waveforms in other steps of the test (Fig. 3b). Second step condition, one point of bi-wire is in contact with water: For obtaining this condition, the water tank of the point 1 was filled with water completely and the tanks of other points remained empty. In other words, the cable was in contact with water just in point 1 (in the distance of 9.4 m from pulse generator). Then, their TDR waveform was recorded. In the TDR waveform, a significant change can be observed in the reflection coefficient values at the interval of 46.19 ns (Fig. 3b). Contact zone of the TDR cable with water at point 1 was detected as a local minimum point in the TDR waveform.

Third step condition, two points of bi-wire are in contact with water: For obtaining this condition, water tanks were filled with water at points 1 and 2 and the tank at the point 3 was left empty. In other words, the bi-wire was placed in contact with water at two points (point 1 and point 2). Then, their TDR waveforms were recorded. The real distance of point 2 from the pulse transmitter was 5.4 m. Two local minimum points can be seen in the TDR waveform, which belongs to these two contact points of the cable with water. These two points was detected in the interval of 47.26 and 26.34 ns from the transmitter (Fig. 3b). The detection error of point 1 location compared with previous step increased up to 3.09%. This was because of the contact of bi-wire with water at point 2. Fourth step condition, three-points of bi-wire are in contact with water: At this step, all the tanks were filled with water, in other words the bi-wire was in contact with water at three points (point 1, point 2, and point 3). In this step of the test, there are three local minimum points in the TDR waveform. The Point 1 was detected in the interval of 47.75 ns, the Point 2 at 26.58 ns, and the Point 3 at 9.28 ns. The positioning error of the point 1 increased up to 4.15 percent compared to the second step of the test. In the second experiment (case 2), first the bi-wire was placed in contact with water in three small positions (Fig. 4a). Then, the

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TDR Unit

Leak point 1

Leak point 2

Leak point 3

A

Leak point 1

Leak point 2

Leak point 3

B " Fig. 4. (a) Schematic diagram showing the second experiment steps (case 2) to investigate the effect of contact length of the TDR sensor with water on the pinpointing accuracy of the leak position 3. (b) TDR waveforms of the different steps of the experiment (In the first step, the three short zones of cable were in contact with water but in steps 2 and 3, the contact length of the cable in simulated positions of 1 and 2 was increased).

length of the cable in contact with water increased in two steps at points 1 and 2 and their TDR waveforms were recorded (Fig. 4b). In other words, to simulate three small leak points, first a biwire cable was crossed through three small tanks filled with water. Then in two steps, the tank dimensions were enlarged at points 1 and 2 in order to increase the length of the cable in contact with water. The main goal of increasing the tank dimensions at these points was to simulate the spread of leakage. In this test, the length of the cable in contact with water were not measured accurately; Therefore, in order to explain the cable length in contact with water, descriptive terms, including short, relatively long and long, were used. Thus, in the second experiment (case 2), TDR measurements were performed in the three different condition: (i) small length of the cable is in contact with water at each three point; (ii) small length of the cable is in contact with water at point 3 but relatively long length of the cable is in contact with water at point 1 and point 2, (iii) small length of the cable is in contact with water at point 3 but long length of the cable is in contact with water at point 1 and point 2, In this test, contact of the cable with water at the point 3 was selected as the target point; therefore, the purpose of this test was to assess the effect of the dimension of the leakage points on the positioning accuracy of the target point, namely the point 3. Based on the results, in the first step of the test, the point 3 were in the interval of 56.97 ns from the transmitter. In the second step, by increasing the contact length of TDR cable with water in points 1 and 2, the interval increased to 57.7 ns and in the third step, with

a further increase of the contact length of the TDR cable with water at points 1 and 2, the time interval rose to 58 ns (Fig. 4b). In other words, with changing the contact length of TDR cable with water from short to long at points 1 and 2, the positioning error of the system at point 3 increased about 1.8%. Evaluation of the position of the leaks To calculate the position of the leakage points, the time data should be converted to distance. To do this, two main steps must be carried out for processing the data: (i) The first step, elimination of the unnecessary data: At this step, only the data associated with the bi-wire cable is required and the data belonging to before and after the bi-wire will be removed. In all the reflectograms in the previous section, only the required data is provided and the unnecessary data has been removed. (ii) The second step, converting the time data to the distance: All graphs and TDR data are based on reflection coefficient against time. Time can be converted to the distance through following equation.

D ¼ V cable

t 2

ð7Þ

where t is the pulse travel time; and Vcable is the pulse transmission speed in the bi-wire. Since the time data is related to the signal sweep, then the expression t/2 is used in the equation. All the TDR waveforms in this study were provided as reflection coefficient against the t/2. The electromagnetic wave moves with speed of the light in the

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vacuum environment, but in other environments, its propagation speed is less. As calculated in Section ‘Description of the Apparatus’, the electromagnetic wave moves with the 68% of the light speed in the bi-wire used in this study, which is equal to 20.5 cm per nanoseconds. Thus, using the above equation, it is possible to convert the given time data to the distance and determine the position of the leakage points. The above processing steps were applied to the data obtained from laboratory tests, the results of which are as follows:

Point 3

For the first test (case 1), the data processing results are displayed in Fig. 5 and Table 1. Based on these results, in the first step of the test, TDR detected the location of point 1 accurately with approximate error of 0.74% (Table 1). In other words, the detection error of the point 1 was about 0.07 m. But when the cable was in contact with water at points 1 and 2, the positioning error of the point 1 was about 0.29 m, and when the cable was in contact with water at three points, the positioning error of the point 1 reached to approximately 0.39 m.

Point 2

Point 1

Fig. 5. Estimation of leakage location for the first experiment (case 1) based on Eq. (7).

Table 1 Effect of the number of leak points on the positioning accuracy of simulated leak point1. Summarized result for leak point 1 Test step

Description of the test step

Real length (m)

Calculated length (m)

Error

Step 1 Step 2 Step 3

One point of the cable is in contact with the water Two points of the cable are in contact with the water Three point of the cable are in contact with water

9.4 9.4 9.4

9.47 9.69 9.79

0.74% 3.09% 4.15%

Leak point 1

Leak point 2

Leak point 3

Fig. 6. Estimation of leakage location for the second experiment (case 2) based on Eq. (7).

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S.M. Fatemi Aghda et al. / Results in Physics 8 (2018) 939–948 Table 2 Effect of the contact length of the TDR sensor with water on the positioning accuracy of leak point 3. Summarized result for leak point 3 Test steps

Description of the test step

Real length (m)

Calculated length (m)

Error

Step 1 Step 2 Step 3

Three short zones of cable are in contact with water Relatively long length of cable is in contact with water in points 1 and 2 Long length of cable is in contact with water in points 1 and 2

11.45 11.45 11.45

11.68 11.83 11.89

2.01% 3.32% 3.84%

The data processing results for the second experiment (case 2) are shown in Fig. 6 and Table 2. Based on these results, when the contact length of the cable with water in three simulated leak points is small, the positioning error of point 3 is approximately 0.23 m, and by increase of the contact length of the cable with water in points 1 and 2 from small to long, the positioning error of point 3 increases to approximately 0.44 m. The most important results from the above experiments are as follows: (i) The simultaneous appearance of several leak points between TDR unit and the location of the leak point under consideration (target point) affect the accuracy of TDR-based water leak detection system negatively. Perhaps this is the most

significant limitation of the TDR application in detecting the leak location. (ii) Increasing the contact length of the TDR sensor with water at the leak points between the TDR unit and the target leak point reduces the accuracy of the water leak detection system based on TDR. Discussion on processed experimental result and accuracy improvement of TDR-based localization system in multiple leak conditions In the preceding sections, it was mentioned that contact of TDR cable with water reduces the speed of electromagnetic wave. In the above tests for calculating the distance of leakage locations from

Steps of creating the reference point by increasing the distance between conductors 1. Increasing the distance between two conductors

2. Placing dielectric material between two conductors

3. Sealing

A

Measured distance of reference point from TDR unit before installation

reffrence point posion 1 posion 2 posion 3 posion 4 posion 5

real distance (m) 1.35 3.7 5.7 7.7 9.7

Change points= Reference

B Fig. 7. Change in the geometry of the bi-wire in order to create reference points (identifiable points in reflectogram).

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TDR device, the wave speed was assumed to be constant in the whole length of the cable. In this case, the distance of the leak location from the TDR unit was calculated using Eq. (7). Eq. (7) calculates the location of leak points accurately when the TDR sensor is in contact with water in just one point. Thus, when the cable is in contact with water in multiple points, only the calculated distance for the closest leak point to the pulse generator will be accurate. For other leak points the precision of positioning will be affected by the leak points between target point and pulse generator. The results of tests conducted by the authors also confirmed the above results. In the first test (case1), by increasing the number of contact points of TDR cables with water, the error rate of positioning of point 1 reached from 0.74 percent to 4.15 percent, and in the whole stages, the lowest error rate of positioning corresponds to the nearest point to the TDR unit. As the results of above test indicated, by increasing the number of contact points of the TDR sensors with water, and by increasing the contact length of the sensor with water at those points, the error rate of TDR system increases. Therefore, the authors tried to improve the accuracy of TDR system in terms of multiple leak condition. In normal mode, there are two reference and definite points for every TDR waveform, which are the beginning and the end points of the cable (Fig. 2). The authors defined some other reference points in the waveform using some changes in specific points of the cable. In this way, the cable virtually was divided into several parts. Since the cable reflections coefficient is a function of the

cable geometry, the authors produced these reflections in specific lengths by changing the cable geometry. The pulse reflection of contact points of cable with water in TDR reflectogram is always negative and downward (local minimum). The authors, to avoid complexity in the analysis, decided to make positive and upward reflections for reference points (local maximum). This was done via increasing the distance between two conductors of the bi-wire cable slightly and placing a dielectric material with specified thickness between them (based on the Eq. (6)). These changes created in five points of the cable (Fig. 7a). TDR waveform, before and after the change in the cable geometry and table of the actual distance of these points from TDR unit are shown in Fig. 7b. Then, the cable was placed in contact with water in 4 positions and their waveform were recorded. Finally, the location of the simulated leak points was calculated using the Eq. (7) (Fig. 8). Only the calculated distance to the leak point1 (the closest position to the pulse transmitter) was accurate and the positioning accuracy of other leak points was affected by decrease of the transmission speed of TDR pulse at the contact points of bi-wire with water (Fig. 8 & Table 3). As the number of leak point increases, the length of the cable appears to increase. So it is completely logical that the maximum error occurs at the farthest leak point, i.e. the leak point 4 (Fig. 8 & Table 3). The authors developed below equation to obtain the actual distance to the leak points based on reference points.

dreal ¼ dreff þ ðt leak  treff Þv cable

ð8Þ

Reference point

TDR Unit

Leak point

Leak posion 1

Leak posion 2

Leak posion 3

Leak posion 4

Fig. 8. Reflectograms of TDR cable with and without reference points; (a) Base reading (no point of the cable is in contact with water). (b) Reflectograms of TDR cable with four leak points. (c) Reflectograms of TDR cable with five point of artificial changes in characteristic impedance and four simulated leakage points.

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S.M. Fatemi Aghda et al. / Results in Physics 8 (2018) 939–948 Table 3 Evaluation the accuracy of suggested method. Leak position

Real distance

Apparent distance D ¼ V cable 2t

Modified calculated distance with reference point d ¼ dreff þ ðt leak  t reff Þv cable

Eapp %

Emod %

Position Position Position Position

2.4 6.25 8.55 11.45

2.39 6.28 8.74 11.75

2.39 6.27 8.58 11.51

0.42% 0.48% 2.22% 2.62%

0.42% 0.32% 0.34% 0.51%

1 2 3 4

TDR Unit

Ground surface

Soil

Reference point Lead cable Leakage position

Pipe

Bi-wire

d reff =real distance to reference point Reference point reflection Leak point reflection

t reff =pulse travel time for reference point

t leak = pulse travel time for leak point

Reflection coefficient

Schematic wave form

Time Fig. 9. Schematization of presented method by the author.

where dreal is the distance to the leak point; dreff is the distance to the nearest reference point before the target leak point (distance to this point must be measured before installation); tleak is the time related to the leak point in the TDR reflectogram; treff is the time related to the reference point in the TDR reflectogram; and Vcable is the wave speed propagation in the bi-wire. As seen in Table 3, the positioning error value for leak point 4 based on the Eq. (7) is approximately 2.62%, while using the equation developed by the authors, the error value is approximately 0.5%. The nearest reference point to the leak point 4 is the reference point 5 that its distance from TDR unit is about 9.7 m. The calculated distance to the leak points based on the Eq. (7), the adjusted distance based on the Eq. (8), and the error value of both equations for all simulated leak points are shown in the Table 3. The results represented the good accuracy of this technique to estimate the true distance of the leak points while there are multiple leaks simultaneously. The field application of the above method has been shown in Fig. 9 schematically. This figure shows the typical apparatus of the TDR based leak localization system. Basically, while the water pipe is being installed, a bi-wire is buried with the pipe. In this figure, the parameters defined in Eq. (8) are also

displayed for one hypothetical leak point. For pinpointing the leak, the operator connects the TDR instrument to the lead cable, which remains accessible through a manhole or through an inspection well. Basically, the bi-wire with reference points and the surrounding soil represent a transmission line, along which the TDR signal can be propagated. Using the method presented by the author, an accurate time continuous method for leak detection by a cheap bi-wire is provided, therefore this method could be reasonable in terms of time, cost and, accuracy.

Conclusion In this research, the authors first conducted a series of experiments to study the effect of the number of leak points and leakage expansion on the precision of TDR-base leak localization system. The accuracy improvement of pinpointing the contact locations of TDR cable with water in multiple leaks condition was the main objective of this study. The results showed that the more the number of contact points of TDR cable with water, the less the accuracy

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of TDR-base leak detection system. Also, the result of the experiments showed that with change of contact length of TDR cable with water from short to long, the pinpointing error of the system increased about 1.83%. The authors created some reference points on the bi-wire using some changes on bi-wire geometry. The reflection of reference point should be easily detected on the TDR waveform. In fact, they divided the cable into several parts virtually. If a leakage appeared in any parts, its location measured using the reference point on that piece independently. Therefore, the leakage appearance in the previous parts could not affect the accuracy of the calculations in considered piece. Finally, an equation was developed to calculate the leakage locations based on the reference points and the results of tests showed the accuracy of the suggested method. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.rinp.2018.01.027. References [1] Tucciarelli T, Criminisi A, Termini D. Leak analysis in pipeline system by means of optimal value regulation. J Hydraul Eng 1999;125(3):277–85. [2] Covas D, Ramos H. Case studies of leak detection and location in water pipe systems by inverse transient analysis. J Water Resour Plann Manage 2010;136 (2):248–57. [3] First Report on Sustainable Use of Water. European Environmental Agency, Copenhagen; 1999. [4] Ekuakille AL, Vendramin G, Trotta A. Spectral analysis of leak detection in a zigzag pipeline: a filter diagonalization method-based algorithm application. Measurement 2009;42(3):358–67. [5] Thornton J, Sturm R, Kunkel G. Water loss control, 2nd ed.; 2008. [6] Hunaidi O, Chu W, Wang A, Guan W. Detecting leaks in plastic pipes. J Am Water Works Assoc (AWWA) 2000;92(2):82–94. [7] Bose JR, Olson MK. TAPS’s leak detection seeks greater precision. Oil Gas J, April 5, p. 43–47. [8] Turner NC. Hardware and software techniques for pipeline integrity and leak detection monitoring. In: Proceedings of Offshore Europe 91, Aberdeen, Scotland; 1991. [9] Zhang J. Designing a cost effective and reliable pipeline leak detection system. Pipeline Reliability Conference; 1996. p. 19–22. [10] Cataldo A, De Benedetto E, Cannazza G, Monti G, Demitri C. Accuracy improvement in the TDR-based localization of water leaks. J Results Phys 2016;6:594–8. [11] Cataldo A, Cannazza G, De Benedetto E, Piuzzi E. Extending industrial applicability of TDR liquid level monitoring through flexible probes. In: 2013 IEEE International Instrumentation and measurement Technology Conference (I2MTC); 2014, p. 850–54. [12] Thomsen A, Hansen B, Schelde K. Application of TDR to water level measurement. J Hydrol 2000;236(3–4):252–8. [13] Moret D, Lopez MV, Arrue JL. TDR application for automated water level measurement from Mariotte reservoirs in tension disc infiltrometers. J Hydrol 2004;297(1–4):229–35.

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